Two Simple Fast Integration Methods for Large-Scale Dynamic Problems in Engineering

Zhai, Wanming

doi:10.1002/(sici)1097-0207(19961230)39:24<4199::aid-nme39>3.0.co;2-y

Cited by 389 publications

(138 citation statements)

References 10 publications

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“…To achieve the fast solution on the dynamic responses of this large-scale system, the Zhai method [57] is used to numerically integrate the differential equations. However, it is still quite time-consuming if each vehicle is regarded as a 3-D model and the track elasticity is also considered simultaneously, as shown in Figure 3.…”

Section: Solving Methods Of Train-track Coupled Dynamic Modelmentioning

confidence: 99%

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

Liu

Zhai

Wang

2016

Vehicle System Dynamics

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For the long heavy-haul train, the basic principles of the intervehicle interaction and train-track dynamic interaction are analysed firstly. Based on the theories of train longitudinal dynamics and vehicle-track coupled dynamics, a three-dimensional (3-D) dynamic model of the heavy-haul train-track coupled system is established through a modularised method. Specifically, this model includes the subsystems such as the train control, the vehicle, the wheel-rail relation and the line geometries. And for the calculation of the wheel-rail interaction force under the driving or braking conditions, the large creep phenomenon that may occur within the wheel-rail contact patch is considered. For the coupler and draft gear system, the coupler forces in three directions and the coupler lateral tilt angles in curves are calculated. Then, according to the characteristics of the long heavy-haul train, an efficient solving method is developed to improve the computational efficiency for such a large system. Some basic principles which should be followed in order to meet the requirement of calculation accuracy are determined. Finally, the 3-D train-track coupled model is verified by comparing the calculated results with the running test results. It is indicated that the proposed dynamic model could simulate the dynamic performance of the heavy-haul train well. ARTICLE HISTORY

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Section: Solving Methods Of Train-track Coupled Dynamic Modelmentioning

confidence: 99%

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

Liu

Zhai

Wang

2016

Vehicle System Dynamics

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“…Finally, Zhai's method (1996) explicit integration scheme was used for integrating the spatially discretized equations with respect to time (Hughes 2003, Zhai 1996.…”

Section: Solving the Motion Equations Of Modelmentioning

confidence: 99%

Investigating the Influence of Auxiliary Rails on Dynamic Behavior of Railway Transition Zone by a 3D Train-Track Interaction Model

Heydari-Noghabi

Varandas

Esmaeili

et al. 2017

Lat. Am. j. solids struct.

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Abrupt track vertical stiffness variations along railway tracks can lead to increased dynamic loads, asymmetric deformations, damaged track components, and consequently, increased maintenance costs. The junction of slab track and ballasted track is one of the existing areas where vertical track stiffness can suddenly change, therefore requiring a transition zone that smoothes the track stiffness change. One of the methods for constructing the transition zone at the junction of slab and ballasted tracks is to install auxiliary rails along the transition zone. In the present study, the dynamic behavior of this type of transition zone was evaluated by a train-track interaction model. For this purpose, a 3D model of the railway track was made, representing the slab track, the transition zone, and the ballasted track. Then, the modeling results were validated by the results of field tests. Afterwards, in order to study the dynamic behavior of the transition zone with auxiliary rails, different sensitive analyses, such as vehicle speed, vehicle load, number of auxiliary rails and railpad stiffness, were performed with the model. The obtained results showed that the use of auxiliary rails reduced the rail deflection variations along the transition zone from 35% to 28% for low and medium speeds (120, 160, 200 km/h), and from 40% to 33% for high speeds (250, 300 km/h). KeywordsRailway track, transition zone of slab track to ballasted track, auxiliary rails, 3D train-track interaction model.

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“…Solutions of the proposed train-track-bridge dynamics model considering self-weight adopt the explicit integration method suggested in the literature [25].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Effect of Bridge‐Pier Differential Settlement on the Dynamic Response of a High‐Speed Railway Train‐Track‐Bridge System

Zhang

Shan

Xia

2017

Mathematical Problems in Engineering

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A model based on the theory of train-track-bridge coupling dynamics is built in the article to investigate how high-speed railway bridge pier differential settlement can affect various railway performance-related criteria. The performance of the model compares favorably with that of a 3D finite element model and train-track-bridge numerical model. The analysis of the study demonstrates that all the dynamic response for a span of 24 m is slightly larger than that for a span of 32 m. The wheel unloading rate increases with pier differential settlement for all of the calculation conditions considered, and its maximum value of 0.695 is well below the allowable limit. Meanwhile, the vertical acceleration increases with pier differential settlement and train speed, respectively, and the values for a pier differential settlement of 10 mm and speed of 350 km/h exceed the maximum allowable limit stipulated in the Chinese standards. On this basis, a speed limit for the exceeding pier differential settlement is determined for comfort consideration. Fasteners that had an initial tensile force due to pier differential settlement experience both compressive and tensile forces as the train passes through and are likely to have a lower service life than those which solely experience compressive forces.

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Two Simple Fast Integration Methods for Large-Scale Dynamic Problems in Engineering

Cited by 389 publications

References 10 publications

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

Establishment and verification of three-dimensional dynamic model for heavy-haul train–track coupled system

Investigating the Influence of Auxiliary Rails on Dynamic Behavior of Railway Transition Zone by a 3D Train-Track Interaction Model

Effect of Bridge‐Pier Differential Settlement on the Dynamic Response of a High‐Speed Railway Train‐Track‐Bridge System

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